Question

Semiconductor wafers can be processed with H2 gas to change the surface chemistry of the wafer. A wafer is placed in a chamber that operates at 1500 K with a H2 pressure of 10–6 mbar. How many collisions take place per second across the surface of a 4” diameter wafer?

Answer 1

Average velocity <c> = ((8*R*T)/(3.1416* M))^0.5 = ((8*8.314 J K^-1 mol^-1*1500 K)/(3.1416*2.016*10^-3 kg mol^-1))^0.5

<c> = ((99768 J mol^-1)/(6.333*10^-3))^0.5 = (15753671.25)^0.5 = 3969.08 m s^-1

Number of collisions take place per second across the surface of a 4" diameter wafer (Z₁)

Z₁ = ((2)^0.5 * 3.1416*diameter(d)²*<c>*P)/KT (1 bar = 10⁵ pascal or N m^-2)

Z₁ = ((2)^0.5 * 3.1416*(4 m)²*3969.08 m s^-1*10^-6*10^-3*10⁵ N m^-2)/1.38*10^-23JK^-1*1500K

Z₁ = (28.2147 N m s^-1/ 2070*10^-23 J) = 0.0136 *10^-23 s^-1

Number of collisions take place per second across the surface of a 4" diameter wafer (Z₁) = 0.0136 *10^-23 s^-1